Strong convergence of a verlet integrator for the semilinear stochastic wave equation

Lehel Banjai, Gabriel Lord, Jeta Molla

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The full discretization of the semilinear stochastic wave equation is considered. The discontinuous Galerkin finite element method is used in space and analyzed in a semigroup framework, and an explicit stochastic position Verlet scheme is used for the temporal approximation. We study the stability under a CFL condition and prove optimal strong convergence rates of the fully discrete scheme. Numerical experiments illustrate our theoretical results. Further, we analyze and bound the expected energy and numerically show excellent agreement with the energy of the exact solution.

Original languageEnglish
Pages (from-to)1976–2003
Number of pages28
JournalSIAM Journal on Numerical Analysis
Volume59
Issue number4
Early online date15 Jul 2021
DOIs
Publication statusPublished - 2021

Keywords

  • Discontinuous Galerkin finite element method
  • Energy conservation
  • Semilinear stochastic wave equation
  • Stability
  • Stochastic Verlet integration
  • Strong convergence

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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